Continuity mistake: In the scene where Irene and Charlie run after the train there are several discontinuities: 1) The warning cross disappears in the shot where the last car passes. 2) In this shot the last car looks much higher than when Irene jumps on. 3) The sun direction changes. (00:55:20)
Continuity mistake: At the health food restaurant Hank gets annoyed with a slurping kid. At this point his hands change between holding on to his chair to lying on the table. (00:57:00)
Continuity mistake: In the motel scene Charlie gets two cokes. When he returns we see Irene taking off her left shoe twice from different camera angles. (01:11:45)
Continuity mistake: During the outside motel scene, there is a maroon car parked outside. It changes between a Ford Escort and a Dodge Intrepid. (01:12:50 - 01:20:10)
Continuity mistake: When we see the policeman with the chicken stuck in his rear end there are more chicken in the background. They disappear a few seconds later. (01:20:10)
Continuity mistake: When Dickie is in Hank's and Irene's train cabin, Irene hits him over the head and he lands on top of Hank. You can see his head is behind Hanks shoulder, but when Hank wakes up Dicky's head is next to Hanks. (01:25:45)
Continuity mistake: When Hank/Charlie fights himself on the platform the station clock shows 3:50 while Charlie's watch shows 5:55 when he throttles himself. (01:28:05)
Continuity mistake: When Charlie/Hank and Irene arrive at the train station in Rhode Island. Charlie and Hank are having a "fight", during this fight Hank unzips his pants to wiggle his "thing" at a group of ladies sitting on a bench. Immediately after that he falls to the ground and his pants are zipped. (01:28:40)
Continuity mistake: In the scene where Charlie is being chased through the train station and gets shot in the arm look out for a boy in the train station with a green top because immediately after he exits the station the boy is sitting on a bench outside. (01:29:45)
Continuity mistake: In the scene where both Jim's characters are beating each other at the wheel of this red convertible, bad Jim throws good Jim out of the car which was doing some 30/40 mph in a straight line. In the next shot Jim is seen chasing the car on foot: the convertible is now doing no more than 7/10 mph and it's descending a hill after a sharp right-hand corner. (01:32:05)
Continuity mistake: The blood comes flowing out of Charlie's hand before he gets his thumb shot off. (01:35:55)
Continuity mistake: After Charlie's thumb has been shot off he dives into the water to rescue Irene. When he reaches out for her with his left hand the thumb is back in place. (01:37:00)
Continuity mistake: Right after Charlie and Irene push the car over the cliff, Charlie asks Irene if she grabbed the wallet off the dash and she says no. Later in the motel, when they are lying in bed, Charlie is sharing family pictures with Irene and they talk about carrying pictures in their wallets. Charlie's was at the bottom of the lake with the car. [The deleted scene on the DVD doesn't really help - in it Hank jumps off the cliff to get his wallet, and then Irene follows. However the movie shows Charlie and Irene looking down the 30 meter high cliff and walking away with dry clothes. Deleted scenes can "disallow" a mistake only if they fill in plausible back story, rather than contradicting the "proper" movie directly.]
Continuity mistake: When Irene and Charlie are in the water near the end, the clouds change between each shot.
Continuity mistake: Just as Charlie reaches Dickie and Irene on the bridge, Dickie is looking forward. In the next shot he is looking down and behind him.
Continuity mistake: Right near the end of the movie when Irene is saying goodbye to Charlie, her makeup is a lot darker to when she is driving away in the car, it looks a lot lighter and rubbed off. When she is pulled over again by the police and gets out of the car her makeup is once again a lot darker.
Continuity mistake: The movie starts out in the present and then flashes back. The skinny trees in front of the house are tall in the beginning and in the flashback they are small. They grow a little more every time it's been a few years, but when they come back to the present, the trees are still only half grown in one shot. In the next, they are fully grown.
Continuity mistake: At the very end when Whitey and the boys are looking for Charley's finger, they are splashing around in a very muddy river, but from the underwater shots the water is quite clear.
Continuity mistake: When Hank/Charlie fall into the car near the end his feet are inside the car. When the shot changes his feet are on the outside.
Continuity mistake: When Charlie is choking the cow the sun changes between shots.
Answer: It's called 'The world ain't slowing down' by Paul Ellis.